FWIW, your private home network WiFi, and the additional public WiFi hot spot that your gateway broadcasts are two completely separate networks. Just because the public hotspot can be accessed does not mean that your password-protected private home network can be accessed.
Yes I agree, FWIU a hot spot does not allow access to your home network but it is using your connectivity. This does not mean there is not other nefarious activities going on. I feel safer with mine off.
FWIW, the public hotspot is a separate and dedicated service flow / bandwidth allocation from the modem. It does not affect or reduce the private service flow / allocation.